A couple of people doing the 23 Things have mentioned that they would like their blog to appear anonymous to anyone reading it. This is how you can change your Display Name if you are using Blogger:
Login to the Google Dashboard (after racking your brains to remember your Google username and password that when you set the account up you knew you'd definitely remember...) and scroll down to the Blogger section. On the right side is an option to edit Blogger Profile. Click on that, then change your Display Name to whatever you want it to be.
I've gone from being anonymous to having my name displayed, partly so I could test that changing it worked, and partly because it felt rude to leave anonymous comments on other blogs!